Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def check(arr, arr_size, sum):
    s = set()
    if(sum%2==0 and sum//2 in arr):
        return True
    for i in range(0, arr_size):
        temp = sum-arr[i]
        if (temp in s):
            return True
        s.add(arr[i])    
    return False        
a=[]
l=0
for i in range(1,150000):
    a.append(i+l)
    l+=i
x=int(input())
print("YES" if check(a,len(a),x) else "NO")